Competing risks arise when individuals may experience multiple mutually exclusive event types. Competing events are frequently treated as censoring and analysed using Kaplan--Meier (KM) methods, which overestimate real-world event risks. While the existence of KM overestimation is well known, its determinants, magnitude, and inferential properties remain poorly characterised. We develop a nonparametric framework that treats competing risks overestimation as a statistical quantity in its own right. We show that competing event frequency alone is insufficient to characterise KM overestimation and develop an event ordering theory describing how temporal event allocation influences overestimation. Based on these results, we derive a closed-form Total Overestimation Diagnostic (TOD) that quantifies total KM overestimation directly from routine survival analysis output. We establish exact error equivalence results for both cause-specific and total overestimation. In particular, Product Limit Error Equivalence shows that inference for TOD reduces exactly to ordinary overall survival estimation. Simulation experiments validate the theoretical results and show that independent censoring primarily affects precision rather than overestimation magnitude. Across six benchmark competing risks datasets, cause-specific overestimation is characterised by both total overestimation and temporal event allocation. These results provide a practical framework for assessing competing risks relevance and determining when cumulative incidence methods should be preferred to naïve KM risks. The proposed framework transforms competing risks overestimation from a qualitative warning into a measurable quantity that can be routinely quantified, interpreted, and incorporated into reporting practice.

翻译：暂无翻译